Reconstruction of signals with unknown spectra in information field theory with parameter uncertainty
| Autor: | Mona Frommert, Torsten A. Ensslin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
FOS: Computer and information sciences
Nuclear and High Energy Physics Cosmology and Nongalactic Astrophysics (astro-ph.CO) Gaussian Computer Science - Information Theory FOS: Physical sciences Image processing Information theory Signal Methodology (stat.ME) symbols.namesake Quantum mechanics Instrumentation and Methods for Astrophysics (astro-ph.IM) Statistics - Methodology Physics Signal reconstruction Information Theory (cs.IT) Estimator Filter (signal processing) Physics - Data Analysis Statistics and Probability symbols Astrophysics - Instrumentation and Methods for Astrophysics Algorithm Data Analysis Statistics and Probability (physics.data-an) Jeffreys prior Astrophysics - Cosmology and Nongalactic Astrophysics |
| Popis: | The optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters. If these are not known a priori, they have to be measured simultaneously from the same data used for the signal reconstruction. We formulate the general problem of signal inference in the presence of unknown parameters within the framework of information field theory. We develop a generic parameter uncertainty renormalized estimation (PURE) technique and address the problem of reconstructing Gaussian signals with unknown power-spectrum with five different approaches: (i) separate maximum-a-posteriori power spectrum measurement and subsequent reconstruction, (ii) maximum-a-posteriori power reconstruction with marginalized power-spectrum, (iii) maximizing the joint posterior of signal and spectrum, (iv) guessing the spectrum from the variance in the Wiener filter map, and (v) renormalization flow analysis of the field theoretical problem providing the PURE filter. In all cases, the reconstruction can be described or approximated as Wiener filter operations with assumed signal spectra derived from the data according to the same recipe, but with differing coefficients. All of these filters, except the renormalized one, exhibit a perception threshold in case of a Jeffreys prior for the unknown spectrum. Data modes, with variance below this threshold do not affect the signal reconstruction at all. Filter (iv) seems to be similar to the so called Karhune-Loeve and Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology, which therefore should also exhibit a marginal perception threshold if correctly implemented. We present statistical performance tests and show that the PURE filter is superior to the others. 21 pages, 5 figures, accepted by PRD |
| Databáze: | OpenAIRE |
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